For the harmonic frequencies f_n = n v / (2L), if n doubles, what happens to f_n?

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Multiple Choice

For the harmonic frequencies f_n = n v / (2L), if n doubles, what happens to f_n?

Explanation:
The harmonic frequencies scale linearly with the mode number. Since f_n = n v /(2L), doubling n gives f_(2n) = (2n v)/(2L) = 2 (n v /(2L)) = 2 f_n. So the frequency doubles. This also fits the idea that harmonics are integer multiples of the fundamental f1 = v/(2L); doubling the harmonic index doubles the frequency. (If you look at wavelengths, λ_n = 2L/n, so doubling n halves the wavelength.)

The harmonic frequencies scale linearly with the mode number. Since f_n = n v /(2L), doubling n gives f_(2n) = (2n v)/(2L) = 2 (n v /(2L)) = 2 f_n. So the frequency doubles. This also fits the idea that harmonics are integer multiples of the fundamental f1 = v/(2L); doubling the harmonic index doubles the frequency. (If you look at wavelengths, λ_n = 2L/n, so doubling n halves the wavelength.)

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